GENERALIZED RELATIONSHIPS

The relationships discussed so far describe situations in which the end of an activity is a necessary condition to begin a successor. Since the relationship links the finish of the predecessor to the start of the successor, all relationships discussed so far are of the finish-to-start (FS) type. This type of relationship is by far the most commonly used in any precedence diagram. In fact, many schedulers use only thesetraditional relationships to build their networks.

The FS relationship is only one of four possible ways in which two activities can be related. It is possible that the start of an activity is a condition for the start of a follower, in what is called a start-to-start (SS) relationship. Similarly, the finish of an activity can constrain the finish of another in a finish-to-finish (FF) relationship. Even another possibility is that the start of an activity constrains the finish of another in a start-to-finish (SF) relationship. This section discusses these more generalized ways to relate the activities in a precedence diagram.

1A discussion of the small gas station schedule using an alternative method, called arrow notation, is presented in Appendix E.

8.5 Generalized Relationships 127

Table 8.1 Durations of Activities for the Small Gas Station

Duration

Activity Title (Days)

1 Mobilize 10

2 Obtain permits 15

3 Site work 8

4 Exterior utilities 12

5 Excavate catch basin 2

6 Excavate footers 5

7 Excavate foundation piers 6

8 Pour footers, etc. 8

9 Erect bldg. frame 10

10 Exterior brick facade 14

11 Exterior fascia panels 4

12 Roof construction 15

13 Landscaping 12

14 Pour interior slabs 10

15 Glazing and doors 6

16 Interior walls 10

17 Elec. & mech. Systems 25

18 Shelves 3

19 Floor coverings 6

20 Interior finishes 8

21 Final inspection 1

22 Demobilization 3

1. Mobilize

Weeks*

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2. Obtain Permits 3. Site Work 4. Ext. Utilities 5. Exc. Catch Basin 6. Exc. Footers 7. Exc. Fdn. Piers 8. Pour Footers 9. Erect Bldg. Frame 10. Ext. Brick Façade 11. Ext. Fascia Panels 12. Roof Construction 13. Landscaping 14. Pour Int. Slabs 15. Glazing & Doors 16. Interior Walls 17. Elec. & Mech. Systems 18. Shelves

19. Floor Coverings 20. Interior Finishes 21. Final Inspection 22. Demobilization

*Weeks are assumed to be work weeks consisting of 5 working days.

Figure 8.13 Expanded bar-net schedule for the small gas station.

8.5.1 Finish-to-Start Relationships

Sometimes, traditional FS relationships are inefficient to model the relation between two activities, even when the finish of the predecessor is a condition for the start of the successor. For example, in any project involving cast-in-place concrete, the concrete is poured and then allowed to cure for a number of days before its formwork can be stripped.

The traditional solution to model the time between the end of the pouring operation and the start of the form-stripping operation is to include a third activity between them to account for the curing period, as shown in Figure 8.14(a).

Although this traditional solution is effective in projects with a few concrete pours, it is impractical for project with many pours. The number of activities in the precedence network for a multistory building with hundreds of pours would be increased by these concrete curing time activities that are included just to delay the start of the form-stripping activities. An alternative to this solution is to include a lag time (or simply, LAG) in the arrow relating pouring and stripping, replacing the concrete curing time activity. As shown in Figure 8.14(b), the start of the stripping activity is the same in the traditional and the lagged alternatives. The relationship used is still of type FS, but it cannot be categorized as traditional anymore.

8.5.2 Start-to-Start Relationships

SS relationships are used when a successor activity must begin after at least a LAG number of days after the start of the predecessor activity. The first segment of a long pipe can be laid before its trench is completely finished. All that is required is that the laying begins when an appropriate length of trench is available. This could be modeled using traditional FS relationships, as shown in Figure 8.15(a). The excavation is broken in two segments so that pipe laying can begin midway into the activity. This solution is not only wasteful by creating an additional activity, but it is also confusing because it implies that the excavation has two stages. In fact, the excavation is totally independent of the succeeding pipe laying.

Compare this traditional solution with Figure 8.15(b) showing the same scenario with an SS relationship with lag time. The solution is more elegant and intuitive than its traditional counterpart.

8.5.3 Finish-to-Finish Relationships

This type of relationship signifies that the successor activity must be finished after at least the number of days indicated in the LAG between the two activities. The previous example of the trenching and pipe laying operation is also applicable here. Suppose that the trenching operation takes 7 days and the pipe must finish at least 3 days after the excavation has been completed. Traditional relationships can depict this condition, as shown in

Pour (a) Using with traditional relationships

(b) Using a lagged FS relationship 5

Figure 8.14 Modeling the sequence of concrete pour-cure-stripping.

8.5 Generalized Relationships 129

Figure 8.16(a). As in the previous cases, this solution is confusing and inefficient. The FF relationship shown in Figure 8.16(b) would be more efficient and elegant. An FF relationship requires the finish of the successor to occur at least LAG days after the finish of the predecessor. The relationship does not indicate that pipe layingmust end 3 days after the trench has been finished. It indicates that the pipe laying must be finishedat least 3 days after the trench is available.

Excavation I 3 days

Lay conduit 8 days Excavation II

4 days

Excavation 7 days

Lay conduit 8 days (a) Using traditional relationships

(b) Using an SS relationship 3

Figure 8.15 Start-to-Start (SS) relationships.

Excavation 7 days

Lay conduit I 5 days

Lay conduit II 3 days

Excavation 7 days

Lay conduit 8 days (a) Using traditional relationships

(b) Using an FF relationship 3

Figure 8.16 Finish-to-Finish relationships.

8.5.4 Activities with Multiple Mutual Relationships

Two activities can have more than one mutual relationship, as long as the relationships specify different types of conditions, and the predecessor–successor relation is not swapped. The same two activities can be related by, say, an SS and an FF relationship, as previously discussed in the example of the pipe laying and trenching activities. But if a relationship indicates that activity A is the predecessor of Activity B, then another cannot indicate that B precedes A. Figure 8.17 shows the double relationships between trenching and pipe laying for the example previously discussed. Notice that in this case, a double relationship is the only way to express the two conditions desired for the previous SS and FF examples. The FF alone implies that the pipe could be laid after at least 1 day of beginning the excavation; the SS alone does satisfy the condition of ending at least 3 days after the excavation is completed. However, field conditions could extend the planned duration of the excavation to, say, 11 days. In such case, the SS relationship would lead to the nonsensical conclusion that the pipe can finish before the excavation. The start and finish dates of the successor are always determined by the relationship that ‘‘pushes’’ it farther in the timeline. This means that only one of the relationships will drive the scheduling of the successor. It is tempting but unwise to remove all nondriving relation-ships to simplify the precedence diagram. As the project gets underway, the assumptions about durations and lags may be changed. An originally nondriving relationship may end up being crucial for the project.